When a crack interacts with material heterogeneities, its front distorts and adopts complex tortuous configurations that are reminiscent of the energy barriers encountered during crack propagation. As such, the study of crack front deformations is key to rationalizing the effective failure properties of micro-structured solids and interfaces and can help predict the occurrence of out-of-plane damage. Current models neglect the influence of a finite dissipation length scale behind the crack tip, called the process zone size. We provide a theoretical framework for quasi-static and dynamic crack-front deformations in heterogeneous cohesive materials and show that the presence of a process zone results in introducing scale effects in the deformation of the crack front. It makes the front more compliant to small-wavelength perturbation but also smooths out fluctuations of strength and process zone size. We numerically validate this theoretical framework with dynamic crack front deformation simulations of co-planar crack propagation. Our work provides a unified framework to predict the deformation of cracks front even when the small-scale yielding hypothesis of linear elastic fracture mechanics breaks down, a key step toward identifying the effective properties of a microstructure.